We aim to reduce the burden of programming and deploying autonomous systems to work in concert with people in time-critical domains such as military field operations and disaster response. Deployment plans for these operations are frequently negotiated on-the-fly by teams of human planners. A human operator then translates the agreed-upon plan into machine instructions for the robots. We present an algorithm that reduces this translation burden by inferring the final plan from a processed form of the human team's planning conversation. Our hybrid approach combines probabilistic generative modeling with logical plan validation used to compute a highly structured prior over possible plans, enabling us to overcome the challenge of performing inference over a large solution space with only a small amount of noisy data from the team planning session. We validate the algorithm through human subject experimentations and show that it is able to infer a human team's final plan with 86% accuracy on average. We also describe a robot demonstration in which two people plan and execute a first-response collaborative task with a PR2 robot. To the best of our knowledge, this is the first work to integrate a logical planning technique within a generative model to perform plan inference.

Annealed importance sampling (AIS) is a common algorithm to estimate partition functions of useful stochastic models. One important problem for obtaining accurate AIS estimates is the selection of an annealing schedule. Conventionally, an annealing schedule is often determined heuristically or is simply set as a linearly increasing sequence. In this paper, we propose an algorithm for the optimal schedule by deriving a functional that dominates the AIS estimation error and by numerically minimizing this functional. We experimentally demonstrate that the proposed algorithm mostly outperforms conventional scheduling schemes with large quantization numbers.

Prior design is one of the most important problems in both statistics and machine learning. The cross validation (CV) and the widely applicable information criterion (WAIC) are predictive measures of the Bayesian estimation, however, it has been difficult to apply them to find the optimal prior because their mathematical properties in prior evaluation have been unknown and the region of the hyperparameters is too wide to be examined. In this paper, we derive a new formula by which the theoretical relation among CV, WAIC, and the generalization loss is clarified and the optimal hyperparameter can be directly found. By the formula, three facts are clarified about predictive prior design. Firstly, CV and WAIC have the same second order asymptotic expansion, hence they are asymptotically equivalent to each other as the optimizer of the hyperparameter. Secondly, the hyperparameter which minimizes CV or WAIC makes the average generalization loss to be minimized asymptotically but does not the random generalization loss. And lastly, by using the mathematical relation between priors, the variances of the optimized hyperparameters by CV and WAIC are made smaller with small computational costs. Also we show that the optimized hyperparameter by DIC or the marginal likelihood does not minimize the average or random generalization loss in general.

Statistical network modeling has focused on representing the graph as a discrete structure, namely the adjacency matrix, and considering the exchangeability of this array. In such cases, the Aldous-Hoover representation theorem (Aldous, 1981;Hoover, 1979} applies and informs us that the graph is necessarily either dense or empty. In this paper, we instead consider representing the graph as a measure on $\mathbb{R}_+^2$. For the associated definition of exchangeability in this continuous space, we rely on the Kallenberg representation theorem (Kallenberg, 2005). We show that for certain choices of such exchangeable random measures underlying our graph construction, our network process is sparse with power-law degree distribution. In particular, we build on the framework of completely random measures (CRMs) and use the theory associated with such processes to derive important network properties, such as an urn representation for our analysis and network simulation. Our theoretical results are explored empirically and compared to common network models. We then present a Hamiltonian Monte Carlo algorithm for efficient exploration of the posterior distribution and demonstrate that we are able to recover graphs ranging from dense to sparse--and perform associated tests--based on our flexible CRM-based formulation. We explore network properties in a range of real datasets, including Facebook social circles, a political blogosphere, protein networks, citation networks, and world wide web networks, including networks with hundreds of thousands of nodes and millions of edges.

Convolutional neural network (CNN) is a neural network that can make use of the internal structure of data such as the 2D structure of image data. This paper studies CNN on text categorization to exploit the 1D structure (namely, word order) of text data for accurate prediction. Instead of using low-dimensional word vectors as input as is often done, we directly apply CNN to high-dimensional text data, which leads to directly learning embedding of small text regions for use in classification. In addition to a straightforward adaptation of CNN from image to text, a simple but new variation which employs bag-of-word conversion in the convolution layer is proposed. An extension to combine multiple convolution layers is also explored for higher accuracy. The experiments demonstrate the effectiveness of our approach in comparison with state-of-the-art methods.

This paper is concerned about sparse, continuous frequency estimation in line spectral estimation, and focused on developing gridless sparse methods which overcome grid mismatches and correspond to limiting scenarios of existing grid-based approaches, e.g., $\ell_1$ optimization and SPICE, with an infinitely dense grid. We generalize AST (atomic-norm soft thresholding) to the case of nonconsecutively sampled data (incomplete data) inspired by recent atomic norm based techniques. We present a gridless version of SPICE (gridless SPICE, or GLS), which is applicable to both complete and incomplete data without the knowledge of noise level. We further prove the equivalence between GLS and atomic norm-based techniques under different assumptions of noise. Moreover, we extend GLS to a systematic framework consisting of model order selection and robust frequency estimation, and present feasible algorithms for AST and GLS. Numerical simulations are provided to validate our theoretical analysis and demonstrate performance of our methods compared to existing ones.

We focus on an interpolation method referred to Bayesian reconstruction in this paper. Whereas in standard interpolation methods missing data are interpolated deterministically, in Bayesian reconstruction, missing data are interpolated probabilistically using a Bayesian treatment. In this paper, we address the framework of Bayesian reconstruction and its application to the traffic data reconstruction problem in the field of traffic engineering. In the latter part of this paper, we describe the evaluation of the statistical performance of our Bayesian traffic reconstruction model using a statistical mechanical approach and clarify its statistical behavior.

In this paper, we provide a new neural-network based perspective on multi-task learning (MTL) and multi-domain learning (MDL). By introducing the concept of a semantic descriptor, this framework unifies MDL and MTL as well as encompassing various classic and recent MTL/MDL algorithms by interpreting them as different ways of constructing semantic descriptors. Our interpretation provides an alternative pipeline for zero-shot learning (ZSL), where a model for a novel class can be constructed without training data. Moreover, it leads to a new and practically relevant problem setting of zero-shot domain adaptation (ZSDA), which is the analogous to ZSL but for novel domains: A model for an unseen domain can be generated by its semantic descriptor. Experiments across this range of problems demonstrate that our framework outperforms a variety of alternatives.

Multimodal learning with deep Boltzmann machines (DBMs) is an generative approach to fuse multimodal inputs, and can learn the shared representation via Contrastive Divergence (CD) for classification and information retrieval tasks. However, it is a 2-fan DBM model, and cannot effectively handle multiple prediction tasks. Moreover, this model cannot recover the hidden representations well by sampling from the conditional distribution when more than one modalities are missing. In this paper, we propose a K-fan deep structure model, which can handle the multi-input and muti-output learning problems effectively. In particular, the deep structure has K-branch for different inputs where each branch can be composed of a multi-layer deep model, and a shared representation is learned in an discriminative manner to tackle multimodal tasks. Given the deep structure, we propose two objective functions to handle two multi-input and multi-output tasks: joint visual restoration and labeling, and the multi-view multi-calss object recognition tasks. To estimate the model parameters, we initialize the deep model parameters with CD to maximize the joint distribution, and then we use backpropagation to update the model according to specific objective function. The experimental results demonstrate that the model can effectively leverages multi-source information and predict multiple tasks well over competitive baselines.

We extend the theory of matrix completion to the case where we make Poisson observations for a subset of entries of a low-rank matrix. We consider the (now) usual matrix recovery formulation through maximum likelihood with proper constraints on the matrix $M$, and establish theoretical upper and lower bounds on the recovery error. Our bounds are nearly optimal up to a factor on the order of $\mathcal{O}(\log(d_1 d_2))$. These bounds are obtained by adapting the arguments used for one-bit matrix completion \cite{davenport20121} (although these two problems are different in nature) and the adaptation requires new techniques exploiting properties of the Poisson likelihood function and tackling the difficulties posed by the locally sub-Gaussian characteristic of the Poisson distribution. Our results highlight a few important distinctions of Poisson matrix completion compared to the prior work in matrix completion including having to impose a minimum signal-to-noise requirement on each observed entry. We also develop an efficient iterative algorithm and demonstrate its good performance in recovering solar flare images.